The aim of this survey is to serve as an introduction to the different techniques available in
the broad field of aggregation-diffusion equations. We aim to provide historical context, key …

We investigate the applicability and efficiency of the invariant subspace method to (2+ 1)-
dimensional time-fractional nonlinear PDEs. We show how to find various types of invariant …

The bi-parabolic equation has many practical significance in the field of heat transfer. The
objective of the paper is to provide a regularized problem for bi-parabolic equation when the …

In this work, we propose an implicit finite-difference scheme to approximate the solutions of
a generalization of the well-known Klein–Gordon–Zakharov system. More precisely, the …

We consider a fractional double phase Robin problem involving variable order and variable
exponents. The nonlinearity f is a Carathéodory function satisfying some hypotheses which …

We prove existence of weak solutions of a fractional thin film type equation with linear
mobility in any space dimension and for any order of the equation. The proof is based on a …

We consider a degenerate nonlocal parabolic equation in a one-dimensional domain
introduced to model hydraulic fractures. The nonlocal operator is given by a fractional power …

In this paper, we study fractional subdiffusion fourth parabolic equations containing Caputo
and Caputo-Fabrizio operators. The main results of the paper are presented in two parts. For …

This manuscript is devoted to studying approximations of a coupled Klein–Gordon–
Zakharov system where different orders of fractional spatial derivatives are utilized. The …

In this paper, we discuss existence and finite speed of propagation for the solutions to an
initial-boundary value problem for a family of fractional thin-film equations in a bounded …